To simplify the expression, we'll substitute the values given:
12a - 3b ÷ (12a + 3b) = -3/4
Let's substitute b = -5/6:
12a - 3(-5/6) ÷ (12a + 3(-5/6)) = -3/4
12a + 5/2 ÷ (12a - 5/2) = -3/4
Now, to simplify further, we'll get rid of the fractions by multiplying both sides by the common denominator of 4:
4(12a + 5/2) ÷ 4(12a - 5/2) = -3
48a + 10 ÷ 48a - 10 = -3
Now, we can solve for a:
48a + 10 = -3(48a - 10)
48a + 10 = -144a + 30
48a + 144a = 30 - 10
192a = 20
a = 20/192
a = 5/48
Therefore, the simplified expression is 5/48.
